# Full text: Proceedings International Workshop on Mobile Mapping Technology

```connected through a straight line. The point of greatest departure
from the straight line is examined. If the departure is too large,
the point becomes an anchor point for two straight line-segments.
The procedure then repeats until all points are fitted by line
segments.
However, the seemingly simple algorithm is complicated by the
necessity to determine anchor points. Any new anchor point may
generate a need for two additional anchor points, each within two
separated segments. We use a “first-in-last-out” stack algorithm
to handle the anchor point selection. The algorithm is described
as follows.
Define a minimum departure which determines an anchor
point, say A,
Set a first-in-last-out stack (STK1), then sequentially push
all the points from the first end point (marked as A) to the
second end point (marked as B), set two more first-in-last-
out stacks (STK2 and STK3), and mark STK2 as -,
Push point B into STK3, and then push point A into STK3,
Pop two end points A and B from STK3. If STK3 is NULL,
go to step h),
Pop end point (marked as C) from STK1. If C==B go to
step g),
Calculate the distance d from point C to the line AB. If d
>A, push point B into STK3, and then push point C into
STK3, mark STK2 as +; pop point from STK2, and push the
point into STK1 until STK2 is NULL, go to step c).
Otherwise, push point C into STK2, continue with step e),
If STK2 marked as - , record point A and point C, iterative
pop point from STK2 until STK2 is NULL, go to step d);
else push point B into STK1, let B==C, pop point from
STK2, and push the point into STK1 until STK2 is NULL,
go to step e), and
Discard STK1, STK2 and STK3, then End.
image. The iterative line detection proceeds with the deletion of
recognized lines. It ends when the ratio of global maximum to
medium values in the accumulative array is less than the ratio of
the array size to the image size. Figures 8(a) to (d) are line
extraction results through Hough transformation.
c)
d)
Figure 8 Line extraction through Hough transformation.
4.6 Line Grouping through Perspective Geometry
In theory, a set of parallel lines in 3-D object space converges at
a single point known as the vanishing point when projected into
the image space. Consider a unit sphere centered at one of the
exposure centers, called a Gaussian sphere. A vanishing point
can also be represented as a point on the Gaussian sphere, that is,
a unit vector placed at the perspective center. So, given a vector
Q in the object space, its vanishing point V on the Gaussian
sphere can be computed as
4.5 Hough Transformation for Global Edge Linking
Hough transformation is mainly used here for linking edge pixels
of straight lines. It involves transformation of a line from a
Cartesian coordinate space to a polar coordinate space, in which,
the transformed line is simply a point at coordinates (p,0). A
family of lines passing through a common point maps into the
connected set of points. The main advantage of Hough
transformation is that it is relatively unaffected by gaps in curves
and by noise. For the problem of straight-line detection, Hough
technique organizes points into straight lines by considering all
possible straight lines.
In practice, there are two key points in an algorithm about Hough
transformation. One is in choosing the size of the array; the other
is in determining a threshold to form or exclude corresponding
lines. In our study, we base the size of the array on the image
size. Our experiments show that in order to achieve good
localized line detection, the size should be two'to three times
larger than the size of image. In order to exclude pseudo lines, a
global maximum criterion (rather than local maximum) is
selected to form a line. The longest line segment sharing two end
points with detected edge pixels is recognized as a line in the
where M is rotation matrix from the object to image coordinate
system. In particular, suppose the solar azimuth is represented by
0. We have two vectors Q and Q on the sphere
```

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